{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "rolled-vacuum",
   "metadata": {
    "tags": []
   },
   "source": [
    "<center><h1>矩阵特征值计算：幂法与反幂法<h1/><center/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "radical-round",
   "metadata": {
    "tags": [],
    "toc-hr-collapsed": true
   },
   "source": [
    "## 实验内容\n",
    "给定矩阵\n",
    "\n",
    "$$\n",
    "A = \\begin{pmatrix}5&4&1&1\\\\4&5&1&1\\\\1&1&4&2\\\\1&1&2&4\\end{pmatrix}\n",
    "$$\n",
    "\n",
    "(1)用幂法求$A$的主特征值及对应的特征向量，并用瑞利商加速方法观察加速效果\n",
    "\n",
    "(2)利用反幂法迭代，使用不同的$p$值，求$A$的不同特征向量及特征向量.比较结果"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "compatible-sense",
   "metadata": {
    "tags": []
   },
   "source": [
    "## 实验原理\n",
    "### 幂法\n",
    "\n",
    "#### 迭代与收敛原理\n",
    "\n",
    "对于初始向量$v_0\\neq0$,设$x_i$是$A$的特征向量，$\\lambda_i$是$A$的特征值\n",
    "$$\n",
    "v_0=\\sum_{i=1}^n\\alpha_i x_i\n",
    "$$\n",
    "构造迭代序列$\\{v_k\\}$与$\\{u_k\\}$\n",
    "\n",
    "$$\n",
    "u_0=v_0\n",
    "$$\n",
    "\n",
    "$$\n",
    "v_k=Au_{k-1},u_k=\\frac{v_k}{abs \\max{\\{v_k\\}}}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "v_k\n",
    "&=\\frac{A^kv_0}{abs\\max{\\{A^{k-1}v_0\\}}}\\\\\n",
    "&=\\frac{\\sum_{i=1}^n\\alpha_i \\lambda_i^k x_i}{abs\\max\\{\\sum_{i=1}^n\\alpha_i \\lambda_i^{k-1} x_i\\}}\\\\\n",
    "&=\\lambda_1\\frac{\\alpha_1x_1+\\sum_{i=2}^n\\alpha_i (\\frac{\\lambda_i}{\\lambda_1})^k x_i}{abs\\max\\{\\alpha_1x_1+\\sum_{i=2}^n\\alpha_i (\\frac{\\lambda_i}{\\lambda_1})^{k-1} x_i\\}}\\\\\n",
    "abs\\max\\{v_k\\}&=\\frac{\\lambda_1abs\\max\\{\\alpha_1x_1+\\sum_{i=2}^n\\alpha_i (\\frac{\\lambda_i}{\\lambda_1})^k x_i\\}}{abs\\max\\{\\alpha_1x_1+\\sum_{i=2}^n\\alpha_i (\\frac{\\lambda_i}{\\lambda_1})^{k-1} x_i\\}}\\rightarrow\\lambda_1\\quad(k\\rightarrow \\infty)\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "#### 算法描述\n",
    "\n",
    "对于给定的初始向量$v_0$与误差要求精度$\\epsilon$\n",
    "$$\n",
    "u\\leftarrow v_0,\\lambda\\leftarrow0\n",
    "$$\n",
    "loop\n",
    "\n",
    "1. $v\\leftarrow Au$\n",
    "2. $u\\leftarrow v/absmax(v)$\n",
    "3. $\\lambda'\\leftarrow absmax(v),\\Delta\\lambda\\leftarrow abs(\\lambda'-\\lambda)$\n",
    "4. if $\\Delta\\lambda<\\epsilon$, then return $\\lambda'$\n",
    "5. $\\lambda\\leftarrow\\lambda'$\n",
    "\n",
    "### 瑞利商加速\n",
    "\n",
    "迭代序列与幂法一致\n",
    "$$\n",
    "v_k=Au_{k-1},u_k=\\frac{v_k}{abs\\max{\\{v_k\\}}}\n",
    "$$\n",
    "\n",
    "其区别在于$\\lambda_1$的逼近表达式\n",
    "$$\n",
    "\\lambda_1 \\leftarrow \\frac{(Au_k,u_k)}{(u_k,u_k)}\\quad(k\\rightarrow\\infty)\n",
    "$$\n",
    "\n",
    "> 所以在编程中`幂法`与`瑞利商法`的代码除了$\\lambda_1$的逼近表达式是一样的，所以可以将$\\lambda_1$的逼近表达式作为参数传入，从而在一个函数中实现\n",
    "\n",
    "### 反幂法\n",
    "\n",
    "对于$p$，若$(A-pI)^{-1}$存在，其特征值为\n",
    "$$\n",
    "\\frac1{\\lambda_i-p}\n",
    "$$\n",
    "对应的特征向量为$x_i$\n",
    "\n",
    "对$(A-pI)^{-1}$使用幂法\n",
    "$$\n",
    "\\begin{cases}\n",
    "u_0=v_0\\neq0&v_0为初始向量\\\\\n",
    "v_k=(A-pI)^{-1}u_{k-1}&k=1,2,\\cdots\\\\\n",
    "u_k=\\frac{v_k}{abs\\max{\\{v_k\\}}}\n",
    "\\end{cases}\n",
    "$$\n",
    "若$p \\rightarrow \\lambda_j$\n",
    "$$\n",
    "|\\lambda_j-p|<<|\\lambda_i-p|,\\quad i\\neq j\n",
    "$$\n",
    "$$\n",
    "\\left|\\frac1{\\lambda_j-p}\\right|>\\left|\\frac1{\\lambda_i-p}\\right|,\\quad\\forall i\\neq j\n",
    "$$\n",
    "说明$\\frac1{\\lambda_j-p}$是主特征值\n",
    "$$\n",
    "\\frac1{\\lambda_j-p}\\leftarrow abs\\max\\{v_k\\},\\quad(k\\rightarrow\\infty)\n",
    "$$\n",
    "$$\n",
    "\\lambda_j\\leftarrow p+\\frac1{abs\\max\\{v_k\\}},\\quad(k\\rightarrow\\infty)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "according-reasoning",
   "metadata": {},
   "source": [
    "## 编程实现\n",
    "> 用Julia语言实现"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "valid-siemens",
   "metadata": {},
   "source": [
    "先导入依赖和输入计算所需的数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "chubby-heart",
   "metadata": {},
   "outputs": [],
   "source": [
    "import Logging\r\n",
    "Logging.disable_logging(Logging.Info)\r\n",
    "\r\n",
    "using LinearAlgebra,Plots\r\n",
    "plotly()\r\n",
    "\r\n",
    "include(\"../Code/MatrixKit.jl\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "outer-discretion",
   "metadata": {},
   "source": [
    "### 幂法和瑞利商法求主特征值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bigger-convergence",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "MainEigen (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "absmax(v) = maximum(abs,v)\r\n",
    "norm!(v) = v ./ absmax(v)\r\n",
    "\r\n",
    "PowerλExpr(A,u,v) = absmax(v)\r\n",
    "RayleighλExpr(A,u,v) = sum(A*u.*u)/sum(u.*u)\r\n",
    "\r\n",
    "function MainEigen(A::Matrix;λexpr=PowerλExpr,u=NaN,digits=4,maxiter=100,reqλs=false)\r\n",
    "    n = size(A)[1]\r\n",
    "    u == NaN || (u = ones(n))  \r\n",
    "    λ = 0.\r\n",
    "    reqλs && (λs = Vector{Float64}())\r\n",
    "    for i ∈ 1:maxiter\r\n",
    "        v = A*u\r\n",
    "        u = norm!(v)\r\n",
    "        λ⁺ = λexpr(A,u,v)\r\n",
    "        ok = false\r\n",
    "        abs(λ⁺-λ) < .1^digits && (ok = true)\r\n",
    "        λ = λ⁺\r\n",
    "        reqλs && push!(λs,λ)\r\n",
    "        if ok\r\n",
    "            if reqλs\r\n",
    "                return λ,u,λs\r\n",
    "            end\r\n",
    "            return λ,u\r\n",
    "        end\r\n",
    "    end\r\n",
    "    (throw∘error)(\"Can't find solution satisfied precise demand within the maximum number of iterations.\")\r\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "preceding-journey",
   "metadata": {},
   "source": [
    "### 反幂法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "established-maria",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "InvPowMethod (generic function with 1 method)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function InvPowMethod(A::Matrix,p::Number;λexpr=PowerλExpr,u=NaN,digits=4,maxiter=100,reqλs=false)\r\n",
    "    n = size(A)[1]\r\n",
    "    u == NaN || (u = ones(n))\r\n",
    "    B⁻¹ = inv(A - p*I)\r\n",
    "    λ = 0.\r\n",
    "    reqλs && (λs = Vector{Float64}())\r\n",
    "    for i ∈ 1:maxiter\r\n",
    "        v = B⁻¹*u\r\n",
    "        u = norm!(v)\r\n",
    "        λ⁺ = p+1/λexpr(B⁻¹,u,v)\r\n",
    "        ok = false\r\n",
    "        abs(λ⁺-λ) < .1^digits && (ok = true)\r\n",
    "        λ = λ⁺\r\n",
    "        reqλs && push!(λs,λ)\r\n",
    "        if ok\r\n",
    "            if reqλs\r\n",
    "                return λ,u,λs\r\n",
    "            end\r\n",
    "            return λ,u\r\n",
    "        end\r\n",
    "    end\r\n",
    "    (throw∘error)(\"Can't find solution satisfied precise demand within the maximum number of iterations.\")\r\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "familiar-alabama",
   "metadata": {},
   "source": [
    "## 计算实例、数据、结果、比较\n",
    "先输入数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "antique-andrew",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "<center>$A=\\begin{pmatrix}5&4&1&1\\\\4&5&1&1\\\\1&1&4&2\\\\1&1&2&4\\end{pmatrix}$</center>\n",
       "\n"
      ],
      "text/markdown": [
       "<center>$A=\\begin{pmatrix}5&4&1&1\\\\4&5&1&1\\\\1&1&4&2\\\\1&1&2&4\\end{pmatrix}$</center>\n"
      ],
      "text/plain": [
       "  <center>\u001b[35mA=\\begin{pmatrix}5&4&1&1\\\\4&5&1&1\\\\1&1&4&2\\\\1&1&2&4\\end{pmatrix}\u001b[39m</center>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@latex A = [[5 4;4 5] ones(Int,2,2);ones(Int,2,2) [4 2;2 4]]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "speaking-making",
   "metadata": {},
   "source": [
    "### 用幂法和瑞利商法计算主特征值\n",
    "#### 计算"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "relative-search",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "λ = 10.000050863147614\n"
     ]
    }
   ],
   "source": [
    "λ,v = MainEigen(A,λexpr=PowerλExpr)\r\n",
    "@show λ;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "floating-growing",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "<center>$v=\\begin{pmatrix}1.0&1.0&0.5000127157222276&0.5000127157222276\\end{pmatrix}^T$</center>\n",
       "\n"
      ],
      "text/markdown": [
       "<center>$v=\\begin{pmatrix}1.0&1.0&0.5000127157222276&0.5000127157222276\\end{pmatrix}^T$</center>\n"
      ],
      "text/plain": [
       "  <center>\u001b[35mv=\\begin{pmatrix}1.0&1.0&0.5000127157222276&0.5000127157222276\\end{pmatrix}^T\u001b[39m</center>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@latex v T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "fundamental-standard",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "λ = 9.999991522909337\n"
     ]
    }
   ],
   "source": [
    "λ,v = MainEigen(A,λexpr=RayleighλExpr)\r\n",
    "@show λ;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "normal-shark",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "<center>$v=\\begin{pmatrix}1.0&1.0&0.501628664495114&0.501628664495114\\end{pmatrix}^T$</center>\n",
       "\n"
      ],
      "text/markdown": [
       "<center>$v=\\begin{pmatrix}1.0&1.0&0.501628664495114&0.501628664495114\\end{pmatrix}^T$</center>\n"
      ],
      "text/plain": [
       "  <center>\u001b[35mv=\\begin{pmatrix}1.0&1.0&0.501628664495114&0.501628664495114\\end{pmatrix}^T\u001b[39m</center>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@latex v T"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "copyrighted-poster",
   "metadata": {},
   "source": [
    "#### 比较\n",
    "这里按照题目要求对两种方法，进行比较\n",
    "\n",
    "下面绘制收敛曲线，来比较一下两种算法收敛速度的差异"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "color-immune",
   "metadata": {},
   "outputs": [
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",
      "text/html": [
       "<!DOCTYPE html>\n",
       "<html>\n",
       "    <head>\n",
       "        <title>Plots.jl</title>\n",
       "        <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n",
       "        \n",
       "    </head>\n",
       "    <body>\n",
       "            <div id=\"1583ec78-69e1-41df-a383-62ec688e3550\" style=\"width:600px;height:400px;\"></div>\n",
       "    <script>\n",
       "        requirejs.config({\n",
       "        paths: {\n",
       "            Plotly: 'https://cdn.plot.ly/plotly-1.57.1.min'\n",
       "        }\n",
       "    });\n",
       "    require(['Plotly'], function (Plotly) {\n",
       "\n",
       "    PLOT = document.getElementById('1583ec78-69e1-41df-a383-62ec688e3550');\n",
       "    Plotly.plot(PLOT, [\n",
       "    {\n",
       "        \"xaxis\": \"x\",\n",
       "        \"colorbar\": {\n",
       "            \"title\": \"\"\n",
       "        },\n",
       "        \"yaxis\": \"y\",\n",
       "        \"x\": [\n",
       "            1,\n",
       "            2,\n",
       "            3,\n",
       "            4,\n",
       "            5,\n",
       "            6,\n",
       "            7,\n",
       "            8,\n",
       "            9,\n",
       "            10,\n",
       "            11,\n",
       "            12,\n",
       "            13,\n",
       "            14,\n",
       "            15\n",
       "        ],\n",
       "        \"showlegend\": true,\n",
       "        \"mode\": \"lines\",\n",
       "        \"name\": \"Power method\",\n",
       "        \"zmin\": null,\n",
       "        \"legendgroup\": \"Power method\",\n",
       "        \"zmax\": null,\n",
       "        \"line\": {\n",
       "            \"color\": \"rgba(0, 154, 250, 1.000)\",\n",
       "            \"shape\": \"linear\",\n",
       "            \"dash\": \"solid\",\n",
       "            \"width\": 1\n",
       "        },\n",
       "        \"y\": [\n",
       "            11.0,\n",
       "            10.454545454545453,\n",
       "            10.217391304347828,\n",
       "            10.106382978723403,\n",
       "            10.05263157894737,\n",
       "            10.026178010471202,\n",
       "            10.013054830287206,\n",
       "            10.006518904823992,\n",
       "            10.003257328990227,\n",
       "            10.001628134158256,\n",
       "            10.000813934559662,\n",
       "            10.000406934158054,\n",
       "            10.000203458799593,\n",
       "            10.000101727330065,\n",
       "            10.000050863147614\n",
       "        ],\n",
       "        \"type\": \"scatter\"\n",
       "    },\n",
       "    {\n",
       "        \"xaxis\": \"x\",\n",
       "        \"colorbar\": {\n",
       "            \"title\": \"\"\n",
       "        },\n",
       "        \"yaxis\": \"y\",\n",
       "        \"x\": [\n",
       "            1,\n",
       "            2,\n",
       "            3,\n",
       "            4,\n",
       "            5,\n",
       "            6,\n",
       "            7,\n",
       "            8\n",
       "        ],\n",
       "        \"showlegend\": true,\n",
       "        \"mode\": \"lines\",\n",
       "        \"name\": \"Rayleigh accelerate method\",\n",
       "        \"zmin\": null,\n",
       "        \"legendgroup\": \"Rayleigh accelerate method\",\n",
       "        \"zmax\": null,\n",
       "        \"line\": {\n",
       "            \"color\": \"rgba(227, 111, 71, 1.000)\",\n",
       "            \"shape\": \"linear\",\n",
       "            \"dash\": \"solid\",\n",
       "            \"width\": 1\n",
       "        },\n",
       "        \"y\": [\n",
       "            9.864864864864863,\n",
       "            9.965517241379311,\n",
       "            9.991334488734834,\n",
       "            9.997830802603037,\n",
       "            9.999457524140176,\n",
       "            9.999864369998644,\n",
       "            9.999966091809819,\n",
       "            9.999991522909337\n",
       "        ],\n",
       "        \"type\": \"scatter\"\n",
       "    }\n",
       "]\n",
       ", {\n",
       "    \"showlegend\": true,\n",
       "    \"xaxis\": {\n",
       "        \"showticklabels\": true,\n",
       "        \"gridwidth\": 0.5,\n",
       "        \"tickvals\": [\n",
       "            0.0,\n",
       "            5.0,\n",
       "            10.0,\n",
       "            15.0\n",
       "        ],\n",
       "        \"range\": [\n",
       "            0.0,\n",
       "            15.0\n",
       "        ],\n",
       "        \"domain\": [\n",
       "            0.10609871682706327,\n",
       "            0.9934383202099737\n",
       "        ],\n",
       "        \"mirror\": false,\n",
       "        \"tickangle\": 0,\n",
       "        \"showline\": true,\n",
       "        \"ticktext\": [\n",
       "            \"0\",\n",
       "            \"5\",\n",
       "            \"10\",\n",
       "            \"15\"\n",
       "        ],\n",
       "        \"zeroline\": false,\n",
       "        \"tickfont\": {\n",
       "            \"color\": \"rgba(0, 0, 0, 1.000)\",\n",
       "            \"family\": \"sans-serif\",\n",
       "            \"size\": 11\n",
       "        },\n",
       "        \"zerolinecolor\": \"rgba(0, 0, 0, 1.000)\",\n",
       "        \"anchor\": \"y\",\n",
       "        \"visible\": true,\n",
       "        \"ticks\": \"inside\",\n",
       "        \"tickmode\": \"array\",\n",
       "        \"linecolor\": \"rgba(0, 0, 0, 1.000)\",\n",
       "        \"showgrid\": true,\n",
       "        \"title\": \"Iterations\",\n",
       "        \"gridcolor\": \"rgba(0, 0, 0, 0.100)\",\n",
       "        \"titlefont\": {\n",
       "            \"color\": \"rgba(0, 0, 0, 1.000)\",\n",
       "            \"family\": \"sans-serif\",\n",
       "            \"size\": 15\n",
       "        },\n",
       "        \"tickcolor\": \"rgb(0, 0, 0)\",\n",
       "        \"type\": \"-\"\n",
       "    },\n",
       "    \"paper_bgcolor\": \"rgba(255, 255, 255, 1.000)\",\n",
       "    \"annotations\": [],\n",
       "    \"height\": 400,\n",
       "    \"margin\": {\n",
       "        \"l\": 0,\n",
       "        \"b\": 20,\n",
       "        \"r\": 0,\n",
       "        \"t\": 20\n",
       "    },\n",
       "    \"plot_bgcolor\": \"rgba(255, 255, 255, 1.000)\",\n",
       "    \"yaxis\": {\n",
       "        \"showticklabels\": true,\n",
       "        \"gridwidth\": 0.5,\n",
       "        \"tickvals\": [\n",
       "            10.0,\n",
       "            10.25,\n",
       "            10.5,\n",
       "            10.75,\n",
       "            11.0\n",
       "        ],\n",
       "        \"range\": [\n",
       "            9.8,\n",
       "            11.0\n",
       "        ],\n",
       "        \"domain\": [\n",
       "            0.07581474190726165,\n",
       "            0.9901574803149606\n",
       "        ],\n",
       "        \"mirror\": false,\n",
       "        \"tickangle\": 0,\n",
       "        \"showline\": true,\n",
       "        \"ticktext\": [\n",
       "            \"10.00\",\n",
       "            \"10.25\",\n",
       "            \"10.50\",\n",
       "            \"10.75\",\n",
       "            \"11.00\"\n",
       "        ],\n",
       "        \"zeroline\": false,\n",
       "        \"tickfont\": {\n",
       "            \"color\": \"rgba(0, 0, 0, 1.000)\",\n",
       "            \"family\": \"sans-serif\",\n",
       "            \"size\": 11\n",
       "        },\n",
       "        \"zerolinecolor\": \"rgba(0, 0, 0, 1.000)\",\n",
       "        \"anchor\": \"x\",\n",
       "        \"visible\": true,\n",
       "        \"ticks\": \"inside\",\n",
       "        \"tickmode\": \"array\",\n",
       "        \"linecolor\": \"rgba(0, 0, 0, 1.000)\",\n",
       "        \"showgrid\": true,\n",
       "        \"title\": \"Main eigenvalue\",\n",
       "        \"gridcolor\": \"rgba(0, 0, 0, 0.100)\",\n",
       "        \"titlefont\": {\n",
       "            \"color\": \"rgba(0, 0, 0, 1.000)\",\n",
       "            \"family\": \"sans-serif\",\n",
       "            \"size\": 15\n",
       "        },\n",
       "        \"tickcolor\": \"rgb(0, 0, 0)\",\n",
       "        \"type\": \"-\"\n",
       "    },\n",
       "    \"legend\": {\n",
       "        \"yanchor\": \"auto\",\n",
       "        \"xanchor\": \"auto\",\n",
       "        \"bordercolor\": \"rgba(0, 0, 0, 1.000)\",\n",
       "        \"bgcolor\": \"rgba(255, 255, 255, 1.000)\",\n",
       "        \"borderwidth\": 1,\n",
       "        \"tracegroupgap\": 0,\n",
       "        \"y\": 1.0,\n",
       "        \"font\": {\n",
       "            \"color\": \"rgba(0, 0, 0, 1.000)\",\n",
       "            \"family\": \"sans-serif\",\n",
       "            \"size\": 11\n",
       "        },\n",
       "        \"title\": {\n",
       "            \"font\": {\n",
       "                \"color\": \"rgba(0, 0, 0, 1.000)\",\n",
       "                \"family\": \"sans-serif\",\n",
       "                \"size\": 15\n",
       "            },\n",
       "            \"text\": \"\"\n",
       "        },\n",
       "        \"traceorder\": \"normal\",\n",
       "        \"x\": 1.0\n",
       "    },\n",
       "    \"width\": 600\n",
       "}\n",
       ");\n",
       "    });\n",
       "    </script>\n",
       "\n",
       "    </body>\n",
       "</html>\n"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_,_,λsᴾ = MainEigen(A,λexpr=PowerλExpr,reqλs=true)\r\n",
    "_,_,λsᴿ = MainEigen(A,λexpr=RayleighλExpr,reqλs=true)\r\n",
    "\r\n",
    "plot(λsᴾ,label=\"Power method\")\r\n",
    "plot!(λsᴿ,label=\"Rayleigh accelerate method\")\r\n",
    "\r\n",
    "xlabel!(\"Iterations\")\r\n",
    "ylabel!(\"Main eigenvalue\")\r\n",
    "ylims!(9.8,11)\r\n",
    "xlims!(0,15)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "protecting-separate",
   "metadata": {},
   "source": [
    "对比，可见`瑞利商加速法`比`幂法`更快更好地收敛\n",
    "\n",
    "当然根据上面计算结果，和迭代公式，可以看出，`瑞利商`只加速了特征值的收敛，并没有加速特征向量的收敛"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "checked-independence",
   "metadata": {},
   "source": [
    "### 用反幂法，选取p，计算全部特征值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "innovative-drama",
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",
      "text/html": [
       "<!DOCTYPE html>\n",
       "<html>\n",
       "    <head>\n",
       "        <title>Plots.jl</title>\n",
       "        <meta http-equiv=\"content-type\" content=\"text/html; charset=UTF-8\">\n",
       "        \n",
       "    </head>\n",
       "    <body>\n",
       "            <div id=\"7d24923f-0265-4b55-adbb-e3e94b618456\" style=\"width:600px;height:400px;\"></div>\n",
       "    <script>\n",
       "        requirejs.config({\n",
       "        paths: {\n",
       "            Plotly: 'https://cdn.plot.ly/plotly-1.57.1.min'\n",
       "        }\n",
       "    });\n",
       "    require(['Plotly'], function (Plotly) {\n",
       "\n",
       "    PLOT = document.getElementById('7d24923f-0265-4b55-adbb-e3e94b618456');\n",
       "    Plotly.plot(PLOT, [\n",
       "    {\n",
       "        \"xaxis\": \"x1\",\n",
       "        \"colorbar\": {\n",
       "            \"title\": \"\"\n",
       "        },\n",
       "        \"yaxis\": \"y1\",\n",
       "        \"x\": [\n",
       "            1,\n",
       "            2,\n",
       "            3,\n",
       "            4,\n",
       "            5,\n",
       "            6,\n",
       "            7,\n",
       "            8,\n",
       "            9,\n",
       "            10,\n",
       "            11,\n",
       "            12,\n",
       "            13,\n",
       "            14,\n",
       "            15\n",
       "        ],\n",
       "        \"showlegend\": false,\n",
       "        \"mode\": \"lines\",\n",
       "        \"name\": \"\",\n",
       "        \"zmin\": null,\n",
       "        \"legendgroup\": \"\",\n",
       "        \"zmax\": null,\n",
       "        \"line\": {\n",
       "            \"color\": \"rgba(0, 154, 250, 1.000)\",\n",
       "            \"shape\": \"linear\",\n",
       "            \"dash\": \"solid\",\n",
       "            \"width\": 1\n",
       "        },\n",
       "        \"y\": [\n",
       "            11.0,\n",
       "            10.454545454545453,\n",
       "            10.217391304347828,\n",
       "            10.106382978723403,\n",
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   "source": [
    "_,_,λsᴾ = MainEigen(A,λexpr=PowerλExpr,reqλs=true)\r\n",
    "_,_,λsᴿ = MainEigen(A,λexpr=RayleighλExpr,reqλs=true)\r\n",
    "\r\n",
    "plotᴾ = plot(λsᴾ,title=\"Normal inverse power method\",label=false)\r\n",
    "plotᴿ = plot(λsᴿ,title=\"with Rayleigh acceleration\",label=false)\r\n",
    "\r\n",
    "resultᴿ = Vector()\r\n",
    "\r\n",
    "for p ∈ 1:10\r\n",
    "    p -= .01\r\n",
    "    _,_,λsᴾ = InvPowMethod(A,p,λexpr=PowerλExpr,reqλs=true)\r\n",
    "    λ,v,λsᴿ = InvPowMethod(A,p,λexpr=RayleighλExpr,reqλs=true)\r\n",
    "    push!(resultᴿ,(p=p,λ=λ,v=round.(v;digits=4)))\r\n",
    "    plot!(plotᴾ,λsᴾ,label=\"p=$p\")\r\n",
    "    plot!(plotᴿ,λsᴿ,label=\"p=$p\")\r\n",
    "end\r\n",
    "\r\n",
    "xlabel!(plotᴿ,\"Iterations\")\r\n",
    "plot(plotᴾ,plotᴿ,layout = (2, 1),legend=false)\r\n",
    "ylabel!(\"eigenvalue\")\r\n",
    "ylims!(0,11)\r\n",
    "xlims!(0,20)"
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  {
   "cell_type": "markdown",
   "id": "solved-steering",
   "metadata": {},
   "source": [
    "$A$为4阶矩阵，至多有4个不同的实特征值\n",
    "\n",
    "`普通反幂法`取10个$p$计算，最终于收敛于6个解，其中必有不是特征值的解\n",
    "\n",
    "`瑞利商加速反幂法`取10个$p$计算，最终于收敛于4个解，所以这4个解均是其特征值的数值近似解\n",
    "\n",
    "可以看到，`普通反幂法`对$p$的选取较为敏感，只有$p$临近真实解时，从能收敛到真实解，可靠性差"
   ]
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  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "forward-element",
   "metadata": {},
   "outputs": [
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       "<table class=\"data-frame\"><thead><tr><th></th><th>p</th><th>λ</th><th>v</th></tr><tr><th></th><th>Float64</th><th>Float64</th><th>Array…</th></tr></thead><tbody><p>10 rows × 3 columns</p><tr><th>1</th><td>0.99</td><td>1.0</td><td>[1.0, -1.0, 0.0, 0.0]</td></tr><tr><th>2</th><td>1.99</td><td>2.0</td><td>[-0.0001, -0.0001, -0.9997, 1.0]</td></tr><tr><th>3</th><td>2.99</td><td>5.0</td><td>[-0.4979, -0.4979, 1.0, 1.0]</td></tr><tr><th>4</th><td>3.99</td><td>5.0</td><td>[-0.4995, -0.4995, 1.0, 1.0]</td></tr><tr><th>5</th><td>4.99</td><td>5.0</td><td>[-0.5, -0.5, 1.0, 1.0]</td></tr><tr><th>6</th><td>5.99</td><td>5.0</td><td>[-0.4992, -0.4992, 1.0, 1.0]</td></tr><tr><th>7</th><td>6.99</td><td>4.99995</td><td>[-0.495, -0.495, 1.0, 1.0]</td></tr><tr><th>8</th><td>7.99</td><td>10.0001</td><td>[1.0, 1.0, 0.4947, 0.4947]</td></tr><tr><th>9</th><td>8.99</td><td>10.0</td><td>[1.0, 1.0, 0.5017, 0.5017]</td></tr><tr><th>10</th><td>9.99</td><td>10.0</td><td>[1.0, 1.0, 0.5, 0.5]</td></tr></tbody></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ccc}\n",
       "\t& p & λ & v\\\\\n",
       "\t\\hline\n",
       "\t& Float64 & Float64 & Array…\\\\\n",
       "\t\\hline\n",
       "\t1 & 0.99 & 1.0 & [1.0, -1.0, 0.0, 0.0] \\\\\n",
       "\t2 & 1.99 & 2.0 & [-0.0001, -0.0001, -0.9997, 1.0] \\\\\n",
       "\t3 & 2.99 & 5.0 & [-0.4979, -0.4979, 1.0, 1.0] \\\\\n",
       "\t4 & 3.99 & 5.0 & [-0.4995, -0.4995, 1.0, 1.0] \\\\\n",
       "\t5 & 4.99 & 5.0 & [-0.5, -0.5, 1.0, 1.0] \\\\\n",
       "\t6 & 5.99 & 5.0 & [-0.4992, -0.4992, 1.0, 1.0] \\\\\n",
       "\t7 & 6.99 & 4.99995 & [-0.495, -0.495, 1.0, 1.0] \\\\\n",
       "\t8 & 7.99 & 10.0001 & [1.0, 1.0, 0.4947, 0.4947] \\\\\n",
       "\t9 & 8.99 & 10.0 & [1.0, 1.0, 0.5017, 0.5017] \\\\\n",
       "\t10 & 9.99 & 10.0 & [1.0, 1.0, 0.5, 0.5] \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "\u001b[1m10×3 DataFrame\u001b[0m\n",
       "\u001b[1m Row \u001b[0m│\u001b[1m p       \u001b[0m\u001b[1m λ        \u001b[0m\u001b[1m v                                \u001b[0m\n",
       "\u001b[1m     \u001b[0m│\u001b[90m Float64 \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Array…                           \u001b[0m\n",
       "─────┼─────────────────────────────────────────────────────\n",
       "   1 │    0.99   1.0      [1.0, -1.0, 0.0, 0.0]\n",
       "   2 │    1.99   2.0      [-0.0001, -0.0001, -0.9997, 1.0]\n",
       "   3 │    2.99   5.0      [-0.4979, -0.4979, 1.0, 1.0]\n",
       "   4 │    3.99   5.0      [-0.4995, -0.4995, 1.0, 1.0]\n",
       "   5 │    4.99   5.0      [-0.5, -0.5, 1.0, 1.0]\n",
       "   6 │    5.99   5.0      [-0.4992, -0.4992, 1.0, 1.0]\n",
       "   7 │    6.99   4.99995  [-0.495, -0.495, 1.0, 1.0]\n",
       "   8 │    7.99  10.0001   [1.0, 1.0, 0.4947, 0.4947]\n",
       "   9 │    8.99  10.0      [1.0, 1.0, 0.5017, 0.5017]\n",
       "  10 │    9.99  10.0      [1.0, 1.0, 0.5, 0.5]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using DataFrames\r\n",
    "\r\n",
    "DataFrame(resultᴿ)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "compact-mustang",
   "metadata": {},
   "source": [
    "> 以上输出结果为`瑞利商加速的反幂法`求解结果\n",
    "\n",
    "观察可知,$A$的特征值与对应的特征向量\n",
    "\n",
    "| $A$的特征值 $\\lambda$ | 矩阵$A$的对应的特征向量  $v$      |\n",
    "| :----------------: | :-------------------: |\n",
    "| 1              | $[1,-1,0,0]^T$      |\n",
    "| 2              | $[0,0,-1,1]^T$      |\n",
    "| 5              | $[0.5,0.5,-1,-1]^T$ |\n",
    "| 10            | $[0.5,0.5,1,1]^T$   |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "prime-coordinator",
   "metadata": {},
   "source": [
    "## 结果分析\n",
    "\n",
    "实验结果与理论基本相符\n",
    "\n",
    "1. 在求主特征值问题上，`幂法`与`瑞利商加速法`都可以较为准确的主特征值与向量，且`瑞利商加速法`速度更快\n",
    "2. 在反幂法求全部特征值问题上，`普通反幂法`对$p$的选取较为敏感，只有$p$临近真实解时，从能收敛到真实解，可靠性差；而`瑞利商加速的反幂法`却可以更好更快的求解，可靠性较好"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "noted-landing",
   "metadata": {},
   "source": [
    "## 参考文献\n",
    "- [1] 李庆扬，王能超，易大义.数值分析[M].北京：清华大学出版社,2018.12\n",
    "- [2] Julia.Docs:Linear Algebra[EB/OL].https://docs.julialang.org/en/v1/stdlib/LinearAlgebra/"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "coastal-produce",
   "metadata": {},
   "source": [
    "## 结尾\n",
    "\n",
    "放个动画彩蛋,展示一下`反幂法`动态收敛效果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "romance-seven",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"\" />"
      ],
      "text/plain": [
       "Plots.AnimatedGif(\"C:\\\\Users\\\\CreatorFan\\\\Documents\\\\Course\\\\Numerical Analysis\\\\Notebooks\\\\tmp.gif\")"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gr()\r\n",
    "\r\n",
    "function cut(array,from,to)\r\n",
    "    try\r\n",
    "        array[from:to]\r\n",
    "    catch \r\n",
    "        array[from:end]\r\n",
    "    end\r\n",
    "end\r\n",
    "\r\n",
    "@gif for i ∈ 2:25\r\n",
    "    plotᴾ = plot(λsᴾ,title=\"Normal inverse power method\",label=false)\r\n",
    "    plotᴿ = plot(λsᴿ,title=\"with Rayleigh acceleration\",label=false)\r\n",
    "\r\n",
    "    for p ∈ 1:10\r\n",
    "        p -= .01\r\n",
    "        _,_,λsᴾ = InvPowMethod(A,p,λexpr=PowerλExpr,reqλs=true)\r\n",
    "        _,_,λsᴿ = InvPowMethod(A,p,λexpr=RayleighλExpr,reqλs=true)\r\n",
    "        plot!(plotᴾ,cut(λsᴾ,1,i),label=\"p=$p\")\r\n",
    "        plot!(plotᴿ,cut(λsᴿ,1,i),label=\"p=$p\")\r\n",
    "    end\r\n",
    "    \r\n",
    "    xlabel!(plotᴿ,\"Iterations\")\r\n",
    "    plot(plotᴾ,plotᴿ,layout = (2, 1),legend=false)\r\n",
    "    ylabel!(\"eigenvalue\")\r\n",
    "    ylims!(0,11)\r\n",
    "    xlims!(1,i > 10 ? i : 10)\r\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fallen-patent",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Copyright\n",
    "\n",
    "> Copyright 2021 by Algebra-FUN(樊一飞)\n",
    ">\n",
    "> ALL RIGHTS RESERVED."
   ]
  }
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